9514 1404 393
Answer:
2
Step-by-step explanation:
The solutions are ...
p +m|x +n| = k . . . . . given
m|x +n| = k -p . . . . . . subtract p
|x +n| = (k -p)/m = (p -k)/-m . . . . . . must have (p-k)/-m ≥ 0
x = -n ± (p -k)/-m
For the given conditions, m < 0, p > k, we are guaranteed that (p-k)/-m > 0, so there are 2 solutions.
Bar graph
.................
a.)
784
/ \
2 392
/ \
2 196
/ \
2 98
/ \
2 49
/ \
7 7
√784 = 7² × 2^4
= 7² × 4²
= <u>28²</u>
So, √784 = 28
b.)
2025
/ \
3 675
/ \
3 225
/ \
3 75
/ \
3 25
/ \
5 5
2025 = 5² × 3^4
= 5² × 9²
= <u>4</u><u>5</u><u>²</u>
So, √2025 = 45
c.)
9261
/ \
3 3087
/ \
3 1029
/ \
3 343
/ \
7 49
/ \
7 7
9261 = 7³ × 3³
= <u>21³</u>
So, ³√9261 = 21
d.)
46656
/ \
2 23328
/ \
2 11664
/ \
2 5832
/ \
2 2916
/ \
2 1458
/ \
2 729
/ \
3 243
/ \
3 81
/ \
3 27
/ \
3 9
/ \
3 3
46.656 = 2³ × 3³ × 2³ × 3³
= 6³ × 6³
= <u>3</u><u>6</u><u>³</u>
So, ³√46.656 = 36
<em>Hope it helps and is useful</em><em> </em><em>:</em><em>)</em>
Answer:
So, when we solve for x we see that we can make 16 cookies using 1 cup of sugar. Then, yes, as you suggested we could divide 30 cookies by this ratio to see that we need less than 2 cups of sugar to make 30 cookies: And, as you said, this value is less than 2 cups, the value under Quantity B. Good job! I hope this helps :)
Step-by-step explanation:
Answer:
x = 4, x = 8
Step-by-step explanation:
Given
(x - 7)(x - 5) = 3 ← expand factors using FOIL
x² - 12x + 35 = 3 ( subtract 3 from both sides )
x² - 12x + 32 = 0 ← in standard form
(x - 4)(x - 8) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 8 = 0 ⇒ x = 8